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"title": "Largest Color Value in a Directed Graph",
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"content": "<p>There is a <strong>directed graph</strong> of <code>n</code> colored nodes and <code>m</code> edges. The nodes are numbered from <code>0</code> to <code>n - 1</code>.</p>\r\n\r\n<p>You are given a string <code>colors</code> where <code>colors[i]</code> is a lowercase English letter representing the <strong>color</strong> of the <code>i<sup>th</sup></code> node in this graph (<strong>0-indexed</strong>). You are also given a 2D array <code>edges</code> where <code>edges[j] = [a<sub>j</sub>, b<sub>j</sub>]</code> indicates that there is a <strong>directed edge</strong> from node <code>a<sub>j</sub></code> to node <code>b<sub>j</sub></code>.</p>\r\n\r\n<p>A valid <strong>path</strong> in the graph is a sequence of nodes <code>x<sub>1</sub> -> x<sub>2</sub> -> x<sub>3</sub> -> ... -> x<sub>k</sub></code> such that there is a directed edge from <code>x<sub>i</sub></code> to <code>x<sub>i+1</sub></code> for every <code>1 <= i < k</code>. The <strong>color value</strong> of the path is the number of nodes that are colored the <strong>most frequently</strong> occurring color along that path.</p>\r\n\r\n<p>Return <em>the <strong>largest color value</strong> of any valid path in the given graph, or </em><code>-1</code><em> if the graph contains a cycle</em>.</p>\r\n\r\n<p> </p>\r\n<p><strong>Example 1:</strong></p>\r\n\r\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/21/leet1.png\" style=\"width: 400px; height: 182px;\" /></p>\r\n\r\n<pre>\r\n<strong>Input:</strong> colors = "abaca", edges = [[0,1],[0,2],[2,3],[3,4]]\r\n<strong>Output:</strong> 3\r\n<strong>Explanation:</strong> The path 0 -> 2 -> 3 -> 4 contains 3 nodes that are colored <code>"a" (red in the above image)</code>.\r\n</pre>\r\n\r\n<p><strong>Example 2:</strong></p>\r\n\r\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/21/leet2.png\" style=\"width: 85px; height: 85px;\" /></p>\r\n\r\n<pre>\r\n<strong>Input:</strong> colors = "a", edges = [[0,0]]\r\n<strong>Output:</strong> -1\r\n<strong>Explanation:</strong> There is a cycle from 0 to 0.\r\n</pre>\r\n\r\n<p> </p>\r\n<p><strong>Constraints:</strong></p>\r\n\r\n<ul>\r\n\t<li><code>n == colors.length</code></li>\r\n\t<li><code>m == edges.length</code></li>\r\n\t<li><code>1 <= n <= 10<sup>5</sup></code></li>\r\n\t<li><code>0 <= m <= 10<sup>5</sup></code></li>\r\n\t<li><code>colors</code> consists of lowercase English letters.</li>\r\n\t<li><code>0 <= a<sub>j</sub>, b<sub>j</sub> < n</code></li>\r\n</ul>",
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"code": "class Solution {\r\npublic:\r\n int largestPathValue(string colors, vector<vector<int>>& edges) {\r\n \r\n }\r\n};",
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"code": "class Solution(object):\r\n def largestPathValue(self, colors, edges):\r\n \"\"\"\r\n :type colors: str\r\n :type edges: List[List[int]]\r\n :rtype: int\r\n \"\"\"",
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"code": "/**\r\n * @param {string} colors\r\n * @param {number[][]} edges\r\n * @return {number}\r\n */\r\nvar largestPathValue = function(colors, edges) {\r\n \r\n};",
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"code": "# @param {String} colors\r\n# @param {Integer[][]} edges\r\n# @return {Integer}\r\ndef largest_path_value(colors, edges)\r\n \r\nend",
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"code": "impl Solution {\r\n pub fn largest_path_value(colors: String, edges: Vec<Vec<i32>>) -> i32 {\r\n \r\n }\r\n}",
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"code": "(define/contract (largest-path-value colors edges)\r\n (-> string? (listof (listof exact-integer?)) exact-integer?)\r\n\r\n )",
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"hints": [
"Use topological sort.",
"let dp[u][c] := the maximum count of vertices with color c of any path starting from vertex u. (by JerryJin2905)"
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